Phase retrieval is the key to quantitative x-ray phase-contrast imaging. To retrieve the phase image of an x-ray wave field, in general one needs multiple phase-contrast images. We have made a new observation of phase-attenuation duality for soft tissues, and we show how only a single phase-contrast image is needed for successful phase retrieval based on this duality. The phase-retrieval formula based on a single phase-contrast image of inhomogeneous soft tissue is derived and presented. We show the striking enhancement of the tissue contrast in simulated phase images that this new approach produces. © 2005 Optical Society of America.
